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Simplifying 131 = 0.006A2 + -0.02A + 120 Reorder the terms: 131 = 120 + -0.02A + 0.006A2 Solving 131 = 120 + -0.02A + 0.006A2 Solving for variable 'A'. Combine like terms: 131 + -120 = 11 11 + 0.02A + -0.006A2 = 120 + -0.02A + 0.006A2 + -120 + 0.02A + -0.006A2 Reorder the terms: 11 + 0.02A + -0.006A2 = 120 + -120 + -0.02A + 0.02A + 0.006A2 + -0.006A2 Combine like terms: 120 + -120 = 0 11 + 0.02A + -0.006A2 = 0 + -0.02A + 0.02A + 0.006A2 + -0.006A2 11 + 0.02A + -0.006A2 = -0.02A + 0.02A + 0.006A2 + -0.006A2 Combine like terms: -0.02A + 0.02A = 0.00 11 + 0.02A + -0.006A2 = 0.00 + 0.006A2 + -0.006A2 11 + 0.02A + -0.006A2 = 0.006A2 + -0.006A2 Combine like terms: 0.006A2 + -0.006A2 = 0.000 11 + 0.02A + -0.006A2 = 0.000 Begin completing the square. Divide all terms by -0.006 the coefficient of the squared term: Divide each side by '-0.006'. -1833.333333 + -3.333333333A + A2 = 0 Move the constant term to the right: Add '1833.333333' to each side of the equation. -1833.333333 + -3.333333333A + 1833.333333 + A2 = 0 + 1833.333333 Reorder the terms: -1833.333333 + 1833.333333 + -3.333333333A + A2 = 0 + 1833.333333 Combine like terms: -1833.333333 + 1833.333333 = 0.000000 0.000000 + -3.333333333A + A2 = 0 + 1833.333333 -3.333333333A + A2 = 0 + 1833.333333 Combine like terms: 0 + 1833.333333 = 1833.333333 -3.333333333A + A2 = 1833.333333 The A term is -3.333333333A. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333A + 2.777777779 + A2 = 1833.333333 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333A + A2 = 1833.333333 + 2.777777779 Combine like terms: 1833.333333 + 2.777777779 = 1836.111110779 2.777777779 + -3.333333333A + A2 = 1836.111110779 Factor a perfect square on the left side: (A + -1.666666667)(A + -1.666666667) = 1836.111110779 Calculate the square root of the right side: 42.849867103 Break this problem into two subproblems by setting (A + -1.666666667) equal to 42.849867103 and -42.849867103.Subproblem 1
A + -1.666666667 = 42.849867103 Simplifying A + -1.666666667 = 42.849867103 Reorder the terms: -1.666666667 + A = 42.849867103 Solving -1.666666667 + A = 42.849867103 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + A = 42.849867103 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + A = 42.849867103 + 1.666666667 A = 42.849867103 + 1.666666667 Combine like terms: 42.849867103 + 1.666666667 = 44.51653377 A = 44.51653377 Simplifying A = 44.51653377Subproblem 2
A + -1.666666667 = -42.849867103 Simplifying A + -1.666666667 = -42.849867103 Reorder the terms: -1.666666667 + A = -42.849867103 Solving -1.666666667 + A = -42.849867103 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + A = -42.849867103 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + A = -42.849867103 + 1.666666667 A = -42.849867103 + 1.666666667 Combine like terms: -42.849867103 + 1.666666667 = -41.183200436 A = -41.183200436 Simplifying A = -41.183200436Solution
The solution to the problem is based on the solutions from the subproblems. A = {44.51653377, -41.183200436}
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